From f35e0b3d3b9f41bee2f5cc357afcb69e3aadad15 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Fri, 8 Jul 2022 17:39:44 +0200 Subject: Store DLL info in mkinmod objects for performance Thanks to Tomas Kalibera for his analysis of the problem on the r-package-devel mailing list and for the suggestion on how to fix it. See the current benchmark vignette for the new data on mkin 1.1.1 with R 4.2.1, with unprecedented performance. --- docs/404.html | 2 +- docs/articles/FOCUS_L.html | 1176 ++++++++++---------- .../figure-html/unnamed-chunk-6-1.png | Bin 36101 -> 36120 bytes docs/articles/index.html | 2 +- docs/articles/web_only/benchmarks.html | 33 +- docs/articles/web_only/dimethenamid_2018.html | 92 +- docs/authors.html | 6 +- docs/index.html | 2 +- docs/news/index.html | 5 +- docs/pkgdown.yml | 2 +- docs/reference/index.html | 2 +- 11 files changed, 673 insertions(+), 649 deletions(-) (limited to 'docs') diff --git a/docs/404.html b/docs/404.html index 6d48c164..7a6ede72 100644 --- a/docs/404.html +++ b/docs/404.html @@ -32,7 +32,7 @@ mkin - 1.1.0 + 1.1.1 diff --git a/docs/articles/FOCUS_L.html b/docs/articles/FOCUS_L.html index d3918ef4..7d36c77c 100644 --- a/docs/articles/FOCUS_L.html +++ b/docs/articles/FOCUS_L.html @@ -33,7 +33,7 @@ mkin - 1.1.0 + 1.1.1 @@ -105,7 +105,7 @@

Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

-

Last change 18 May 2022 (rebuilt 2022-06-30)

+

Last change 18 May 2022 (rebuilt 2022-07-08)

Source: vignettes/FOCUS_L.rmd @@ -119,197 +119,189 @@

The following code defines example dataset L1 from the FOCUS kinetics report, p. 284:

-library("mkin", quietly = TRUE)
-FOCUS_2006_L1 = data.frame(
-  t = rep(c(0, 1, 2, 3, 5, 7, 14, 21, 30), each = 2),
-  parent = c(88.3, 91.4, 85.6, 84.5, 78.9, 77.6,
-             72.0, 71.9, 50.3, 59.4, 47.0, 45.1,
-             27.7, 27.3, 10.0, 10.4, 2.9, 4.0))
-FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)
+library("mkin", quietly = TRUE) +FOCUS_2006_L1 = data.frame( + t = rep(c(0, 1, 2, 3, 5, 7, 14, 21, 30), each = 2), + parent = c(88.3, 91.4, 85.6, 84.5, 78.9, 77.6, + 72.0, 71.9, 50.3, 59.4, 47.0, 45.1, + 27.7, 27.3, 10.0, 10.4, 2.9, 4.0)) +FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)

Here we use the assumptions of simple first order (SFO), the case of declining rate constant over time (FOMC) and the case of two different phases of the kinetics (DFOP). For a more detailed discussion of the models, please see the FOCUS kinetics report.

Since mkin version 0.9-32 (July 2014), we can use shorthand notation like "SFO" for parent only degradation models. The following two lines fit the model and produce the summary report of the model fit. This covers the numerical analysis given in the FOCUS report.

-m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE)
-summary(m.L1.SFO)
-
## mkin version used for fitting:    1.1.0 
-## R version used for fitting:       4.2.1 
-## Date of fit:     Thu Jun 30 10:43:59 2022 
-## Date of summary: Thu Jun 30 10:43:59 2022 
-## 
-## Equations:
-## d_parent/dt = - k_parent * parent
-## 
-## Model predictions using solution type analytical 
-## 
-## Fitted using 133 model solutions performed in 0.032 s
-## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: OLS 
-## 
-## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 89.85  state
-## k_parent  0.10 deparm
-## 
-## Starting values for the transformed parameters actually optimised:
-##                  value lower upper
-## parent_0     89.850000  -Inf   Inf
-## log_k_parent -2.302585  -Inf   Inf
-## 
-## Fixed parameter values:
-## None
-## 
-## Results:
-## 
-##        AIC     BIC    logLik
-##   93.88778 96.5589 -43.94389
-## 
-## Optimised, transformed parameters with symmetric confidence intervals:
-##              Estimate Std. Error  Lower  Upper
-## parent_0       92.470    1.28200 89.740 95.200
-## log_k_parent   -2.347    0.03763 -2.428 -2.267
-## sigma           2.780    0.46330  1.792  3.767
-## 
-## Parameter correlation:
-##                parent_0 log_k_parent      sigma
-## parent_0      1.000e+00    6.186e-01 -1.516e-09
-## log_k_parent  6.186e-01    1.000e+00 -3.124e-09
-## sigma        -1.516e-09   -3.124e-09  1.000e+00
-## 
-## Backtransformed parameters:
-## Confidence intervals for internally transformed parameters are asymmetric.
-## t-test (unrealistically) based on the assumption of normal distribution
-## for estimators of untransformed parameters.
-##          Estimate t value    Pr(>t)    Lower   Upper
-## parent_0 92.47000   72.13 8.824e-21 89.74000 95.2000
-## k_parent  0.09561   26.57 2.487e-14  0.08824  0.1036
-## sigma     2.78000    6.00 1.216e-05  1.79200  3.7670
-## 
-## FOCUS Chi2 error levels in percent:
-##          err.min n.optim df
-## All data   3.424       2  7
-## parent     3.424       2  7
-## 
-## Estimated disappearance times:
-##         DT50  DT90
-## parent 7.249 24.08
-## 
-## Data:
-##  time variable observed predicted residual
-##     0   parent     88.3    92.471  -4.1710
-##     0   parent     91.4    92.471  -1.0710
-##     1   parent     85.6    84.039   1.5610
-##     1   parent     84.5    84.039   0.4610
-##     2   parent     78.9    76.376   2.5241
-##     2   parent     77.6    76.376   1.2241
-##     3   parent     72.0    69.412   2.5884
-##     3   parent     71.9    69.412   2.4884
-##     5   parent     50.3    57.330  -7.0301
-##     5   parent     59.4    57.330   2.0699
-##     7   parent     47.0    47.352  -0.3515
-##     7   parent     45.1    47.352  -2.2515
-##    14   parent     27.7    24.247   3.4528
-##    14   parent     27.3    24.247   3.0528
-##    21   parent     10.0    12.416  -2.4163
-##    21   parent     10.4    12.416  -2.0163
-##    30   parent      2.9     5.251  -2.3513
-##    30   parent      4.0     5.251  -1.2513
+m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE) +summary(m.L1.SFO) +
## mkin version used for fitting:    1.1.1 
+## R version used for fitting:       4.2.1 
+## Date of fit:     Fri Jul  8 17:34:00 2022 
+## Date of summary: Fri Jul  8 17:34:00 2022 
+## 
+## Equations:
+## d_parent/dt = - k_parent * parent
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 133 model solutions performed in 0.028 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##          value   type
+## parent_0 89.85  state
+## k_parent  0.10 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##                  value lower upper
+## parent_0     89.850000  -Inf   Inf
+## log_k_parent -2.302585  -Inf   Inf
+## 
+## Fixed parameter values:
+## None
+## 
+## Results:
+## 
+##        AIC     BIC    logLik
+##   93.88778 96.5589 -43.94389
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##              Estimate Std. Error  Lower  Upper
+## parent_0       92.470    1.28200 89.740 95.200
+## log_k_parent   -2.347    0.03763 -2.428 -2.267
+## sigma           2.780    0.46330  1.792  3.767
+## 
+## Parameter correlation:
+##                parent_0 log_k_parent      sigma
+## parent_0      1.000e+00    6.186e-01 -1.712e-09
+## log_k_parent  6.186e-01    1.000e+00 -3.237e-09
+## sigma        -1.712e-09   -3.237e-09  1.000e+00
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##          Estimate t value    Pr(>t)    Lower   Upper
+## parent_0 92.47000   72.13 8.824e-21 89.74000 95.2000
+## k_parent  0.09561   26.57 2.487e-14  0.08824  0.1036
+## sigma     2.78000    6.00 1.216e-05  1.79200  3.7670
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   3.424       2  7
+## parent     3.424       2  7
+## 
+## Estimated disappearance times:
+##         DT50  DT90
+## parent 7.249 24.08
+## 
+## Data:
+##  time variable observed predicted residual
+##     0   parent     88.3    92.471  -4.1710
+##     0   parent     91.4    92.471  -1.0710
+##     1   parent     85.6    84.039   1.5610
+##     1   parent     84.5    84.039   0.4610
+##     2   parent     78.9    76.376   2.5241
+##     2   parent     77.6    76.376   1.2241
+##     3   parent     72.0    69.412   2.5884
+##     3   parent     71.9    69.412   2.4884
+##     5   parent     50.3    57.330  -7.0301
+##     5   parent     59.4    57.330   2.0699
+##     7   parent     47.0    47.352  -0.3515
+##     7   parent     45.1    47.352  -2.2515
+##    14   parent     27.7    24.247   3.4528
+##    14   parent     27.3    24.247   3.0528
+##    21   parent     10.0    12.416  -2.4163
+##    21   parent     10.4    12.416  -2.0163
+##    30   parent      2.9     5.251  -2.3513
+##    30   parent      4.0     5.251  -1.2513

A plot of the fit is obtained with the plot function for mkinfit objects.

-plot(m.L1.SFO, show_errmin = TRUE, main = "FOCUS L1 - SFO")
+plot(m.L1.SFO, show_errmin = TRUE, main = "FOCUS L1 - SFO")

The residual plot can be easily obtained by

-mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")
+mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")

For comparison, the FOMC model is fitted as well, and the \(\chi^2\) error level is checked.

-m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)
-
## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:
-## false convergence (8)
-
-plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")
+m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE) +plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")

-
-summary(m.L1.FOMC, data = FALSE)
-
## Warning in sqrt(diag(covar)): NaNs produced
-
## Warning in sqrt(1/diag(V)): NaNs produced
-
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful
-
## mkin version used for fitting:    1.1.0 
-## R version used for fitting:       4.2.1 
-## Date of fit:     Thu Jun 30 10:44:00 2022 
-## Date of summary: Thu Jun 30 10:44:00 2022 
-## 
-## Equations:
-## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
-## 
-## Model predictions using solution type analytical 
-## 
-## Fitted using 369 model solutions performed in 0.082 s
-## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: OLS 
-## 
-## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 89.85  state
-## alpha     1.00 deparm
-## beta     10.00 deparm
-## 
-## Starting values for the transformed parameters actually optimised:
-##               value lower upper
-## parent_0  89.850000  -Inf   Inf
-## log_alpha  0.000000  -Inf   Inf
-## log_beta   2.302585  -Inf   Inf
-## 
-## Fixed parameter values:
-## None
-## 
-## 
-## Warning(s): 
-## Optimisation did not converge:
-## false convergence (8)
-## 
-## Results:
-## 
-##        AIC      BIC   logLik
-##   95.88781 99.44929 -43.9439
-## 
-## Optimised, transformed parameters with symmetric confidence intervals:
-##           Estimate Std. Error  Lower  Upper
-## parent_0     92.47     1.2820 89.720 95.220
-## log_alpha    13.78        NaN    NaN    NaN
-## log_beta     16.13        NaN    NaN    NaN
-## sigma         2.78     0.4598  1.794  3.766
-## 
-## Parameter correlation:
-##            parent_0 log_alpha log_beta     sigma
-## parent_0  1.0000000       NaN      NaN 0.0001671
-## log_alpha       NaN         1      NaN       NaN
-## log_beta        NaN       NaN        1       NaN
-## sigma     0.0001671       NaN      NaN 1.0000000
-## 
-## Backtransformed parameters:
-## Confidence intervals for internally transformed parameters are asymmetric.
-## t-test (unrealistically) based on the assumption of normal distribution
-## for estimators of untransformed parameters.
-##           Estimate t value Pr(>t)  Lower  Upper
-## parent_0 9.247e+01      NA     NA 89.720 95.220
-## alpha    9.658e+05      NA     NA     NA     NA
-## beta     1.010e+07      NA     NA     NA     NA
-## sigma    2.780e+00      NA     NA  1.794  3.766
-## 
-## FOCUS Chi2 error levels in percent:
-##          err.min n.optim df
-## All data   3.619       3  6
-## parent     3.619       3  6
-## 
-## Estimated disappearance times:
-##        DT50  DT90 DT50back
-## parent 7.25 24.08     7.25
+
+summary(m.L1.FOMC, data = FALSE)
+
## Warning in sqrt(diag(covar)): NaNs produced
+
## Warning in sqrt(1/diag(V)): NaNs produced
+
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful
+
## mkin version used for fitting:    1.1.1 
+## R version used for fitting:       4.2.1 
+## Date of fit:     Fri Jul  8 17:34:00 2022 
+## Date of summary: Fri Jul  8 17:34:00 2022 
+## 
+## Equations:
+## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 357 model solutions performed in 0.07 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##          value   type
+## parent_0 89.85  state
+## alpha     1.00 deparm
+## beta     10.00 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##               value lower upper
+## parent_0  89.850000  -Inf   Inf
+## log_alpha  0.000000  -Inf   Inf
+## log_beta   2.302585  -Inf   Inf
+## 
+## Fixed parameter values:
+## None
+## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   95.88804 99.44953 -43.94402
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##           Estimate Std. Error  Lower  Upper
+## parent_0     92.47     1.2820 89.720 95.220
+## log_alpha    11.37        NaN    NaN    NaN
+## log_beta     13.72        NaN    NaN    NaN
+## sigma         2.78     0.4621  1.789  3.771
+## 
+## Parameter correlation:
+##            parent_0 log_alpha log_beta     sigma
+## parent_0  1.0000000       NaN      NaN 0.0005548
+## log_alpha       NaN         1      NaN       NaN
+## log_beta        NaN       NaN        1       NaN
+## sigma     0.0005548       NaN      NaN 1.0000000
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##           Estimate t value Pr(>t)  Lower  Upper
+## parent_0     92.47      NA     NA 89.720 95.220
+## alpha     87110.00      NA     NA     NA     NA
+## beta     911100.00      NA     NA     NA     NA
+## sigma         2.78      NA     NA  1.789  3.771
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   3.619       3  6
+## parent     3.619       3  6
+## 
+## Estimated disappearance times:
+##         DT50  DT90 DT50back
+## parent 7.249 24.08    7.249

We get a warning that the default optimisation algorithm Port did not converge, which is an indication that the model is overparameterised, i.e. contains too many parameters that are ill-defined as a consequence.

And in fact, due to the higher number of parameters, and the lower number of degrees of freedom of the fit, the \(\chi^2\) error level is actually higher for the FOMC model (3.6%) than for the SFO model (3.4%). Additionally, the parameters log_alpha and log_beta internally fitted in the model have excessive confidence intervals, that span more than 25 orders of magnitude (!) when backtransformed to the scale of alpha and beta. Also, the t-test for significant difference from zero does not indicate such a significant difference, with p-values greater than 0.1, and finally, the parameter correlation of log_alpha and log_beta is 1.000, clearly indicating that the model is overparameterised.

The \(\chi^2\) error levels reported in Appendix 3 and Appendix 7 to the FOCUS kinetics report are rounded to integer percentages and partly deviate by one percentage point from the results calculated by mkin. The reason for this is not known. However, mkin gives the same \(\chi^2\) error levels as the kinfit package and the calculation routines of the kinfit package have been extensively compared to the results obtained by the KinGUI software, as documented in the kinfit package vignette. KinGUI was the first widely used standard package in this field. Also, the calculation of \(\chi^2\) error levels was compared with KinGUII, CAKE and DegKin manager in a project sponsored by the German Umweltbundesamt (Ranke 2014).

@@ -318,21 +310,21 @@

Laboratory Data L2

The following code defines example dataset L2 from the FOCUS kinetics report, p. 287:

-
-FOCUS_2006_L2 = data.frame(
-  t = rep(c(0, 1, 3, 7, 14, 28), each = 2),
-  parent = c(96.1, 91.8, 41.4, 38.7,
-             19.3, 22.3, 4.6, 4.6,
-             2.6, 1.2, 0.3, 0.6))
-FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
+
+FOCUS_2006_L2 = data.frame(
+  t = rep(c(0, 1, 3, 7, 14, 28), each = 2),
+  parent = c(96.1, 91.8, 41.4, 38.7,
+             19.3, 22.3, 4.6, 4.6,
+             2.6, 1.2, 0.3, 0.6))
+FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)

SFO fit for L2

Again, the SFO model is fitted and the result is plotted. The residual plot can be obtained simply by adding the argument show_residuals to the plot command.

-
-m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
-plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE,
-     main = "FOCUS L2 - SFO")
+
+m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
+plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE,
+     main = "FOCUS L2 - SFO")

The \(\chi^2\) error level of 14% suggests that the model does not fit very well. This is also obvious from the plots of the fit, in which we have included the residual plot.

In the FOCUS kinetics report, it is stated that there is no apparent systematic error observed from the residual plot up to the measured DT90 (approximately at day 5), and there is an underestimation beyond that point.

@@ -342,169 +334,169 @@

FOMC fit for L2

For comparison, the FOMC model is fitted as well, and the \(\chi^2\) error level is checked.

-
-m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE)
-plot(m.L2.FOMC, show_residuals = TRUE,
-     main = "FOCUS L2 - FOMC")
+
+m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE)
+plot(m.L2.FOMC, show_residuals = TRUE,
+     main = "FOCUS L2 - FOMC")

-
-summary(m.L2.FOMC, data = FALSE)
-
## mkin version used for fitting:    1.1.0 
-## R version used for fitting:       4.2.1 
-## Date of fit:     Thu Jun 30 10:44:01 2022 
-## Date of summary: Thu Jun 30 10:44:01 2022 
-## 
-## Equations:
-## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
-## 
-## Model predictions using solution type analytical 
-## 
-## Fitted using 239 model solutions performed in 0.049 s
-## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: OLS 
-## 
-## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 93.95  state
-## alpha     1.00 deparm
-## beta     10.00 deparm
-## 
-## Starting values for the transformed parameters actually optimised:
-##               value lower upper
-## parent_0  93.950000  -Inf   Inf
-## log_alpha  0.000000  -Inf   Inf
-## log_beta   2.302585  -Inf   Inf
-## 
-## Fixed parameter values:
-## None
-## 
-## Results:
-## 
-##        AIC      BIC    logLik
-##   61.78966 63.72928 -26.89483
-## 
-## Optimised, transformed parameters with symmetric confidence intervals:
-##           Estimate Std. Error    Lower   Upper
-## parent_0   93.7700     1.6130 90.05000 97.4900
-## log_alpha   0.3180     0.1559 -0.04149  0.6776
-## log_beta    0.2102     0.2493 -0.36460  0.7850
-## sigma       2.2760     0.4645  1.20500  3.3470
-## 
-## Parameter correlation:
-##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.828e-09
-## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.602e-07
-## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.372e-07
-## sigma     -7.828e-09 -1.602e-07 -1.372e-07  1.000e+00
-## 
-## Backtransformed parameters:
-## Confidence intervals for internally transformed parameters are asymmetric.
-## t-test (unrealistically) based on the assumption of normal distribution
-## for estimators of untransformed parameters.
-##          Estimate t value    Pr(>t)   Lower  Upper
-## parent_0   93.770  58.120 4.267e-12 90.0500 97.490
-## alpha       1.374   6.414 1.030e-04  0.9594  1.969
-## beta        1.234   4.012 1.942e-03  0.6945  2.192
-## sigma       2.276   4.899 5.977e-04  1.2050  3.347
-## 
-## FOCUS Chi2 error levels in percent:
-##          err.min n.optim df
-## All data   6.205       3  3
-## parent     6.205       3  3
-## 
-## Estimated disappearance times:
-##          DT50  DT90 DT50back
-## parent 0.8092 5.356    1.612
+
+summary(m.L2.FOMC, data = FALSE)
+
## mkin version used for fitting:    1.1.1 
+## R version used for fitting:       4.2.1 
+## Date of fit:     Fri Jul  8 17:34:01 2022 
+## Date of summary: Fri Jul  8 17:34:01 2022 
+## 
+## Equations:
+## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 239 model solutions performed in 0.044 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##          value   type
+## parent_0 93.95  state
+## alpha     1.00 deparm
+## beta     10.00 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##               value lower upper
+## parent_0  93.950000  -Inf   Inf
+## log_alpha  0.000000  -Inf   Inf
+## log_beta   2.302585  -Inf   Inf
+## 
+## Fixed parameter values:
+## None
+## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   61.78966 63.72928 -26.89483
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##           Estimate Std. Error    Lower   Upper
+## parent_0   93.7700     1.6130 90.05000 97.4900
+## log_alpha   0.3180     0.1559 -0.04149  0.6776
+## log_beta    0.2102     0.2493 -0.36460  0.7850
+## sigma       2.2760     0.4645  1.20500  3.3470
+## 
+## Parameter correlation:
+##             parent_0  log_alpha   log_beta      sigma
+## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.637e-09
+## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.617e-07
+## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.387e-07
+## sigma     -7.637e-09 -1.617e-07 -1.387e-07  1.000e+00
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##          Estimate t value    Pr(>t)   Lower  Upper
+## parent_0   93.770  58.120 4.267e-12 90.0500 97.490
+## alpha       1.374   6.414 1.030e-04  0.9594  1.969
+## beta        1.234   4.012 1.942e-03  0.6945  2.192
+## sigma       2.276   4.899 5.977e-04  1.2050  3.347
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   6.205       3  3
+## parent     6.205       3  3
+## 
+## Estimated disappearance times:
+##          DT50  DT90 DT50back
+## parent 0.8092 5.356    1.612

The error level at which the \(\chi^2\) test passes is much lower in this case. Therefore, the FOMC model provides a better description of the data, as less experimental error has to be assumed in order to explain the data.

DFOP fit for L2

Fitting the four parameter DFOP model further reduces the \(\chi^2\) error level.

-
-m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE)
-plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
-     main = "FOCUS L2 - DFOP")
+
+m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE)
+plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
+     main = "FOCUS L2 - DFOP")

-
-summary(m.L2.DFOP, data = FALSE)
-
## mkin version used for fitting:    1.1.0 
-## R version used for fitting:       4.2.1 
-## Date of fit:     Thu Jun 30 10:44:01 2022 
-## Date of summary: Thu Jun 30 10:44:01 2022 
-## 
-## Equations:
-## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
-##            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
-##            * parent
-## 
-## Model predictions using solution type analytical 
-## 
-## Fitted using 581 model solutions performed in 0.132 s
-## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: OLS 
-## 
-## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 93.95  state
-## k1        0.10 deparm
-## k2        0.01 deparm
-## g         0.50 deparm
-## 
-## Starting values for the transformed parameters actually optimised:
-##              value lower upper
-## parent_0 93.950000  -Inf   Inf
-## log_k1   -2.302585  -Inf   Inf
-## log_k2   -4.605170  -Inf   Inf
-## g_qlogis  0.000000  -Inf   Inf
-## 
-## Fixed parameter values:
-## None
-## 
-## Results:
-## 
-##        AIC      BIC    logLik
-##   52.36695 54.79148 -21.18347
-## 
-## Optimised, transformed parameters with symmetric confidence intervals:
-##          Estimate Std. Error      Lower     Upper
-## parent_0   93.950  9.998e-01    91.5900   96.3100
-## log_k1      3.112  1.842e+03 -4353.0000 4359.0000
-## log_k2     -1.088  6.285e-02    -1.2370   -0.9394
-## g_qlogis   -0.399  9.946e-02    -0.6342   -0.1638
-## sigma       1.414  2.886e-01     0.7314    2.0960
-## 
-## Parameter correlation:
-##            parent_0     log_k1     log_k2   g_qlogis      sigma
-## parent_0  1.000e+00  6.783e-07 -3.390e-10  2.665e-01 -2.967e-10
-## log_k1    6.783e-07  1.000e+00  1.116e-04 -2.196e-04 -1.031e-05
-## log_k2   -3.390e-10  1.116e-04  1.000e+00 -7.903e-01  2.917e-09
-## g_qlogis  2.665e-01 -2.196e-04 -7.903e-01  1.000e+00 -4.408e-09
-## sigma    -2.967e-10 -1.031e-05  2.917e-09 -4.408e-09  1.000e+00
-## 
-## Backtransformed parameters:
-## Confidence intervals for internally transformed parameters are asymmetric.
-## t-test (unrealistically) based on the assumption of normal distribution
-## for estimators of untransformed parameters.
-##          Estimate   t value    Pr(>t)   Lower   Upper
-## parent_0  93.9500 9.397e+01 2.036e-12 91.5900 96.3100
-## k1        22.4800 5.553e-04 4.998e-01  0.0000     Inf
-## k2         0.3369 1.591e+01 4.697e-07  0.2904  0.3909
-## g          0.4016 1.680e+01 3.238e-07  0.3466  0.4591
-## sigma      1.4140 4.899e+00 8.776e-04  0.7314  2.0960
-## 
-## FOCUS Chi2 error levels in percent:
-##          err.min n.optim df
-## All data    2.53       4  2
-## parent      2.53       4  2
-## 
-## Estimated disappearance times:
-##          DT50  DT90 DT50back DT50_k1 DT50_k2
-## parent 0.5335 5.311    1.599 0.03084   2.058
+
+summary(m.L2.DFOP, data = FALSE)
+
## mkin version used for fitting:    1.1.1 
+## R version used for fitting:       4.2.1 
+## Date of fit:     Fri Jul  8 17:34:01 2022 
+## Date of summary: Fri Jul  8 17:34:01 2022 
+## 
+## Equations:
+## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+##            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+##            * parent
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 581 model solutions performed in 0.119 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##          value   type
+## parent_0 93.95  state
+## k1        0.10 deparm
+## k2        0.01 deparm
+## g         0.50 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##              value lower upper
+## parent_0 93.950000  -Inf   Inf
+## log_k1   -2.302585  -Inf   Inf
+## log_k2   -4.605170  -Inf   Inf
+## g_qlogis  0.000000  -Inf   Inf
+## 
+## Fixed parameter values:
+## None
+## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   52.36695 54.79148 -21.18347
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##          Estimate Std. Error      Lower     Upper
+## parent_0   93.950  9.998e-01    91.5900   96.3100
+## log_k1      3.113  1.845e+03 -4360.0000 4367.0000
+## log_k2     -1.088  6.285e-02    -1.2370   -0.9394
+## g_qlogis   -0.399  9.946e-02    -0.6342   -0.1638
+## sigma       1.414  2.886e-01     0.7314    2.0960
+## 
+## Parameter correlation:
+##            parent_0     log_k1     log_k2   g_qlogis      sigma
+## parent_0  1.000e+00  6.784e-07 -5.188e-10  2.665e-01 -5.800e-10
+## log_k1    6.784e-07  1.000e+00  1.114e-04 -2.191e-04 -1.029e-05
+## log_k2   -5.188e-10  1.114e-04  1.000e+00 -7.903e-01  5.080e-09
+## g_qlogis  2.665e-01 -2.191e-04 -7.903e-01  1.000e+00 -7.991e-09
+## sigma    -5.800e-10 -1.029e-05  5.080e-09 -7.991e-09  1.000e+00
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##          Estimate   t value    Pr(>t)   Lower   Upper
+## parent_0  93.9500 9.397e+01 2.036e-12 91.5900 96.3100
+## k1        22.4800 5.544e-04 4.998e-01  0.0000     Inf
+## k2         0.3369 1.591e+01 4.697e-07  0.2904  0.3909
+## g          0.4016 1.680e+01 3.238e-07  0.3466  0.4591
+## sigma      1.4140 4.899e+00 8.776e-04  0.7314  2.0960
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data    2.53       4  2
+## parent      2.53       4  2
+## 
+## Estimated disappearance times:
+##          DT50  DT90 DT50back DT50_k1 DT50_k2
+## parent 0.5335 5.311    1.599 0.03083   2.058

Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion.

@@ -512,20 +504,20 @@

Laboratory Data L3

The following code defines example dataset L3 from the FOCUS kinetics report, p. 290.

-
-FOCUS_2006_L3 = data.frame(
-  t = c(0, 3, 7, 14, 30, 60, 91, 120),
-  parent = c(97.8, 60, 51, 43, 35, 22, 15, 12))
-FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3)
+
+FOCUS_2006_L3 = data.frame(
+  t = c(0, 3, 7, 14, 30, 60, 91, 120),
+  parent = c(97.8, 60, 51, 43, 35, 22, 15, 12))
+FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3)

Fit multiple models

As of mkin version 0.9-39 (June 2015), we can fit several models to one or more datasets in one call to the function mmkin. The datasets have to be passed in a list, in this case a named list holding only the L3 dataset prepared above.

-
-# Only use one core here, not to offend the CRAN checks
-mm.L3 <- mmkin(c("SFO", "FOMC", "DFOP"), cores = 1,
-               list("FOCUS L3" = FOCUS_2006_L3_mkin), quiet = TRUE)
-plot(mm.L3)
+
+# Only use one core here, not to offend the CRAN checks
+mm.L3 <- mmkin(c("SFO", "FOMC", "DFOP"), cores = 1,
+               list("FOCUS L3" = FOCUS_2006_L3_mkin), quiet = TRUE)
+plot(mm.L3)

The \(\chi^2\) error level of 21% as well as the plot suggest that the SFO model does not fit very well. The FOMC model performs better, with an error level at which the \(\chi^2\) test passes of 7%. Fitting the four parameter DFOP model further reduces the \(\chi^2\) error level considerably.

@@ -534,96 +526,96 @@

The objects returned by mmkin are arranged like a matrix, with models as a row index and datasets as a column index.

We can extract the summary and plot for e.g. the DFOP fit, using square brackets for indexing which will result in the use of the summary and plot functions working on mkinfit objects.

+
+summary(mm.L3[["DFOP", 1]])
+
## mkin version used for fitting:    1.1.1 
+## R version used for fitting:       4.2.1 
+## Date of fit:     Fri Jul  8 17:34:02 2022 
+## Date of summary: Fri Jul  8 17:34:02 2022 
+## 
+## Equations:
+## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+##            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+##            * parent
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 376 model solutions performed in 0.072 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##          value   type
+## parent_0 97.80  state
+## k1        0.10 deparm
+## k2        0.01 deparm
+## g         0.50 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##              value lower upper
+## parent_0 97.800000  -Inf   Inf
+## log_k1   -2.302585  -Inf   Inf
+## log_k2   -4.605170  -Inf   Inf
+## g_qlogis  0.000000  -Inf   Inf
+## 
+## Fixed parameter values:
+## None
+## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   32.97732 33.37453 -11.48866
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##          Estimate Std. Error   Lower      Upper
+## parent_0  97.7500    1.01900 94.5000 101.000000
+## log_k1    -0.6612    0.10050 -0.9812  -0.341300
+## log_k2    -4.2860    0.04322 -4.4230  -4.148000
+## g_qlogis  -0.1739    0.05270 -0.3416  -0.006142
+## sigma      1.0170    0.25430  0.2079   1.827000
+## 
+## Parameter correlation:
+##            parent_0     log_k1     log_k2   g_qlogis      sigma
+## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -9.632e-08
+## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  7.145e-07
+## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  1.021e-06
+## g_qlogis  4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -7.925e-07
+## sigma    -9.632e-08  7.145e-07  1.021e-06 -7.925e-07  1.000e+00
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##          Estimate t value    Pr(>t)    Lower     Upper
+## parent_0 97.75000  95.960 1.248e-06 94.50000 101.00000
+## k1        0.51620   9.947 1.081e-03  0.37490   0.71090
+## k2        0.01376  23.140 8.840e-05  0.01199   0.01579
+## g         0.45660  34.920 2.581e-05  0.41540   0.49850
+## sigma     1.01700   4.000 1.400e-02  0.20790   1.82700
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   2.225       4  4
+## parent     2.225       4  4
+## 
+## Estimated disappearance times:
+##         DT50 DT90 DT50back DT50_k1 DT50_k2
+## parent 7.464  123    37.03   1.343   50.37
+## 
+## Data:
+##  time variable observed predicted residual
+##     0   parent     97.8     97.75  0.05396
+##     3   parent     60.0     60.45 -0.44933
+##     7   parent     51.0     49.44  1.56338
+##    14   parent     43.0     43.84 -0.83632
+##    30   parent     35.0     35.15 -0.14707
+##    60   parent     22.0     23.26 -1.25919
+##    91   parent     15.0     15.18 -0.18181
+##   120   parent     12.0     10.19  1.81395
-summary(mm.L3[["DFOP", 1]])
-
## mkin version used for fitting:    1.1.0 
-## R version used for fitting:       4.2.1 
-## Date of fit:     Thu Jun 30 10:44:02 2022 
-## Date of summary: Thu Jun 30 10:44:02 2022 
-## 
-## Equations:
-## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
-##            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
-##            * parent
-## 
-## Model predictions using solution type analytical 
-## 
-## Fitted using 376 model solutions performed in 0.08 s
-## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: OLS 
-## 
-## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 97.80  state
-## k1        0.10 deparm
-## k2        0.01 deparm
-## g         0.50 deparm
-## 
-## Starting values for the transformed parameters actually optimised:
-##              value lower upper
-## parent_0 97.800000  -Inf   Inf
-## log_k1   -2.302585  -Inf   Inf
-## log_k2   -4.605170  -Inf   Inf
-## g_qlogis  0.000000  -Inf   Inf
-## 
-## Fixed parameter values:
-## None
-## 
-## Results:
-## 
-##        AIC      BIC    logLik
-##   32.97732 33.37453 -11.48866
-## 
-## Optimised, transformed parameters with symmetric confidence intervals:
-##          Estimate Std. Error   Lower      Upper
-## parent_0  97.7500    1.01900 94.5000 101.000000
-## log_k1    -0.6612    0.10050 -0.9812  -0.341300
-## log_k2    -4.2860    0.04322 -4.4230  -4.148000
-## g_qlogis  -0.1739    0.05270 -0.3416  -0.006142
-## sigma      1.0170    0.25430  0.2079   1.827000
-## 
-## Parameter correlation:
-##            parent_0     log_k1     log_k2   g_qlogis      sigma
-## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -9.664e-08
-## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  7.147e-07
-## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  1.022e-06
-## g_qlogis  4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -7.926e-07
-## sigma    -9.664e-08  7.147e-07  1.022e-06 -7.926e-07  1.000e+00
-## 
-## Backtransformed parameters:
-## Confidence intervals for internally transformed parameters are asymmetric.
-## t-test (unrealistically) based on the assumption of normal distribution
-## for estimators of untransformed parameters.
-##          Estimate t value    Pr(>t)    Lower     Upper
-## parent_0 97.75000  95.960 1.248e-06 94.50000 101.00000
-## k1        0.51620   9.947 1.081e-03  0.37490   0.71090
-## k2        0.01376  23.140 8.840e-05  0.01199   0.01579
-## g         0.45660  34.920 2.581e-05  0.41540   0.49850
-## sigma     1.01700   4.000 1.400e-02  0.20790   1.82700
-## 
-## FOCUS Chi2 error levels in percent:
-##          err.min n.optim df
-## All data   2.225       4  4
-## parent     2.225       4  4
-## 
-## Estimated disappearance times:
-##         DT50 DT90 DT50back DT50_k1 DT50_k2
-## parent 7.464  123    37.03   1.343   50.37
-## 
-## Data:
-##  time variable observed predicted residual
-##     0   parent     97.8     97.75  0.05396
-##     3   parent     60.0     60.45 -0.44933
-##     7   parent     51.0     49.44  1.56338
-##    14   parent     43.0     43.84 -0.83632
-##    30   parent     35.0     35.15 -0.14707
-##    60   parent     22.0     23.26 -1.25919
-##    91   parent     15.0     15.18 -0.18181
-##   120   parent     12.0     10.19  1.81395
-
-plot(mm.L3[["DFOP", 1]], show_errmin = TRUE)
+plot(mm.L3[["DFOP", 1]], show_errmin = TRUE)

Here, a look to the model plot, the confidence intervals of the parameters and the correlation matrix suggest that the parameter estimates are reliable, and the DFOP model can be used as the best-fit model based on the \(\chi^2\) error level criterion for laboratory data L3.

This is also an example where the standard t-test for the parameter g_ilr is misleading, as it tests for a significant difference from zero. In this case, zero appears to be the correct value for this parameter, and the confidence interval for the backtransformed parameter g is quite narrow.

@@ -633,155 +625,155 @@

Laboratory Data L4

The following code defines example dataset L4 from the FOCUS kinetics report, p. 293:

-
-FOCUS_2006_L4 = data.frame(
-  t = c(0, 3, 7, 14, 30, 60, 91, 120),
-  parent = c(96.6, 96.3, 94.3, 88.8, 74.9, 59.9, 53.5, 49.0))
-FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4)
+
+FOCUS_2006_L4 = data.frame(
+  t = c(0, 3, 7, 14, 30, 60, 91, 120),
+  parent = c(96.6, 96.3, 94.3, 88.8, 74.9, 59.9, 53.5, 49.0))
+FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4)

Fits of the SFO and FOMC models, plots and summaries are produced below:

-
-# Only use one core here, not to offend the CRAN checks
-mm.L4 <- mmkin(c("SFO", "FOMC"), cores = 1,
-               list("FOCUS L4" = FOCUS_2006_L4_mkin),
-               quiet = TRUE)
-plot(mm.L4)
+
+# Only use one core here, not to offend the CRAN checks
+mm.L4 <- mmkin(c("SFO", "FOMC"), cores = 1,
+               list("FOCUS L4" = FOCUS_2006_L4_mkin),
+               quiet = TRUE)
+plot(mm.L4)

The \(\chi^2\) error level of 3.3% as well as the plot suggest that the SFO model fits very well. The error level at which the \(\chi^2\) test passes is slightly lower for the FOMC model. However, the difference appears negligible.

+
+summary(mm.L4[["SFO", 1]], data = FALSE)
+
## mkin version used for fitting:    1.1.1 
+## R version used for fitting:       4.2.1 
+## Date of fit:     Fri Jul  8 17:34:02 2022 
+## Date of summary: Fri Jul  8 17:34:02 2022 
+## 
+## Equations:
+## d_parent/dt = - k_parent * parent
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 142 model solutions performed in 0.026 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##          value   type
+## parent_0  96.6  state
+## k_parent   0.1 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##                  value lower upper
+## parent_0     96.600000  -Inf   Inf
+## log_k_parent -2.302585  -Inf   Inf
+## 
+## Fixed parameter values:
+## None
+## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   47.12133 47.35966 -20.56067
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##              Estimate Std. Error  Lower   Upper
+## parent_0       96.440    1.69900 92.070 100.800
+## log_k_parent   -5.030    0.07059 -5.211  -4.848
+## sigma           3.162    0.79050  1.130   5.194
+## 
+## Parameter correlation:
+##               parent_0 log_k_parent     sigma
+## parent_0     1.000e+00    5.938e-01 3.440e-07
+## log_k_parent 5.938e-01    1.000e+00 5.885e-07
+## sigma        3.440e-07    5.885e-07 1.000e+00
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##           Estimate t value    Pr(>t)     Lower     Upper
+## parent_0 96.440000   56.77 1.604e-08 92.070000 1.008e+02
+## k_parent  0.006541   14.17 1.578e-05  0.005455 7.842e-03
+## sigma     3.162000    4.00 5.162e-03  1.130000 5.194e+00
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   3.287       2  6
+## parent     3.287       2  6
+## 
+## Estimated disappearance times:
+##        DT50 DT90
+## parent  106  352
-summary(mm.L4[["SFO", 1]], data = FALSE)
-
## mkin version used for fitting:    1.1.0 
-## R version used for fitting:       4.2.1 
-## Date of fit:     Thu Jun 30 10:44:02 2022 
-## Date of summary: Thu Jun 30 10:44:02 2022 
-## 
-## Equations:
-## d_parent/dt = - k_parent * parent
-## 
-## Model predictions using solution type analytical 
-## 
-## Fitted using 142 model solutions performed in 0.03 s
-## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: OLS 
-## 
-## Starting values for parameters to be optimised:
-##          value   type
-## parent_0  96.6  state
-## k_parent   0.1 deparm
-## 
-## Starting values for the transformed parameters actually optimised:
-##                  value lower upper
-## parent_0     96.600000  -Inf   Inf
-## log_k_parent -2.302585  -Inf   Inf
-## 
-## Fixed parameter values:
-## None
-## 
-## Results:
-## 
-##        AIC      BIC    logLik
-##   47.12133 47.35966 -20.56067
-## 
-## Optimised, transformed parameters with symmetric confidence intervals:
-##              Estimate Std. Error  Lower   Upper
-## parent_0       96.440    1.69900 92.070 100.800
-## log_k_parent   -5.030    0.07059 -5.211  -4.848
-## sigma           3.162    0.79050  1.130   5.194
-## 
-## Parameter correlation:
-##               parent_0 log_k_parent     sigma
-## parent_0     1.000e+00    5.938e-01 3.387e-07
-## log_k_parent 5.938e-01    1.000e+00 5.830e-07
-## sigma        3.387e-07    5.830e-07 1.000e+00
-## 
-## Backtransformed parameters:
-## Confidence intervals for internally transformed parameters are asymmetric.
-## t-test (unrealistically) based on the assumption of normal distribution
-## for estimators of untransformed parameters.
-##           Estimate t value    Pr(>t)     Lower     Upper
-## parent_0 96.440000   56.77 1.604e-08 92.070000 1.008e+02
-## k_parent  0.006541   14.17 1.578e-05  0.005455 7.842e-03
-## sigma     3.162000    4.00 5.162e-03  1.130000 5.194e+00
-## 
-## FOCUS Chi2 error levels in percent:
-##          err.min n.optim df
-## All data   3.287       2  6
-## parent     3.287       2  6
-## 
-## Estimated disappearance times:
-##        DT50 DT90
-## parent  106  352
-
-summary(mm.L4[["FOMC", 1]], data = FALSE)
-
## mkin version used for fitting:    1.1.0 
-## R version used for fitting:       4.2.1 
-## Date of fit:     Thu Jun 30 10:44:02 2022 
-## Date of summary: Thu Jun 30 10:44:03 2022 
-## 
-## Equations:
-## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
-## 
-## Model predictions using solution type analytical 
-## 
-## Fitted using 224 model solutions performed in 0.045 s
-## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: OLS 
-## 
-## Starting values for parameters to be optimised:
-##          value   type
-## parent_0  96.6  state
-## alpha      1.0 deparm
-## beta      10.0 deparm
-## 
-## Starting values for the transformed parameters actually optimised:
-##               value lower upper
-## parent_0  96.600000  -Inf   Inf
-## log_alpha  0.000000  -Inf   Inf
-## log_beta   2.302585  -Inf   Inf
-## 
-## Fixed parameter values:
-## None
-## 
-## Results:
-## 
-##        AIC      BIC    logLik
-##   40.37255 40.69032 -16.18628
-## 
-## Optimised, transformed parameters with symmetric confidence intervals:
-##           Estimate Std. Error   Lower    Upper
-## parent_0   99.1400     1.2670 95.6300 102.7000
-## log_alpha  -0.3506     0.2616 -1.0770   0.3756
-## log_beta    4.1740     0.3938  3.0810   5.2670
-## sigma       1.8300     0.4575  0.5598   3.1000
-## 
-## Parameter correlation:
-##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.468e-07
-## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.478e-08
-## log_beta  -5.543e-01  9.889e-01  1.000e+00  5.211e-08
-## sigma     -2.468e-07  2.478e-08  5.211e-08  1.000e+00
-## 
-## Backtransformed parameters:
-## Confidence intervals for internally transformed parameters are asymmetric.
-## t-test (unrealistically) based on the assumption of normal distribution
-## for estimators of untransformed parameters.
-##          Estimate t value    Pr(>t)   Lower   Upper
-## parent_0  99.1400  78.250 7.993e-08 95.6300 102.700
-## alpha      0.7042   3.823 9.365e-03  0.3407   1.456
-## beta      64.9800   2.540 3.201e-02 21.7800 193.900
-## sigma      1.8300   4.000 8.065e-03  0.5598   3.100
-## 
-## FOCUS Chi2 error levels in percent:
-##          err.min n.optim df
-## All data   2.029       3  5
-## parent     2.029       3  5
-## 
-## Estimated disappearance times:
-##         DT50 DT90 DT50back
-## parent 108.9 1644    494.9
+summary(mm.L4[["FOMC", 1]], data = FALSE) +
## mkin version used for fitting:    1.1.1 
+## R version used for fitting:       4.2.1 
+## Date of fit:     Fri Jul  8 17:34:02 2022 
+## Date of summary: Fri Jul  8 17:34:02 2022 
+## 
+## Equations:
+## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 224 model solutions performed in 0.041 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##          value   type
+## parent_0  96.6  state
+## alpha      1.0 deparm
+## beta      10.0 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##               value lower upper
+## parent_0  96.600000  -Inf   Inf
+## log_alpha  0.000000  -Inf   Inf
+## log_beta   2.302585  -Inf   Inf
+## 
+## Fixed parameter values:
+## None
+## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   40.37255 40.69032 -16.18628
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##           Estimate Std. Error   Lower    Upper
+## parent_0   99.1400     1.2670 95.6300 102.7000
+## log_alpha  -0.3506     0.2616 -1.0770   0.3756
+## log_beta    4.1740     0.3938  3.0810   5.2670
+## sigma       1.8300     0.4575  0.5598   3.1000
+## 
+## Parameter correlation:
+##             parent_0  log_alpha   log_beta      sigma
+## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.563e-07
+## log_alpha -4.696e-01  1.000e+00  9.889e-01  4.066e-08
+## log_beta  -5.543e-01  9.889e-01  1.000e+00  6.818e-08
+## sigma     -2.563e-07  4.066e-08  6.818e-08  1.000e+00
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##          Estimate t value    Pr(>t)   Lower   Upper
+## parent_0  99.1400  78.250 7.993e-08 95.6300 102.700
+## alpha      0.7042   3.823 9.365e-03  0.3407   1.456
+## beta      64.9800   2.540 3.201e-02 21.7800 193.900
+## sigma      1.8300   4.000 8.065e-03  0.5598   3.100
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   2.029       3  5
+## parent     2.029       3  5
+## 
+## Estimated disappearance times:
+##         DT50 DT90 DT50back
+## parent 108.9 1644    494.9

References @@ -811,7 +803,7 @@

-

Site built with pkgdown 2.0.2.

+

Site built with pkgdown 2.0.5.

diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png index b6130527..b56e91e1 100644 Binary files a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png and b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png differ diff --git a/docs/articles/index.html b/docs/articles/index.html index 717c34a8..9cdfa9de 100644 --- a/docs/articles/index.html +++ b/docs/articles/index.html @@ -17,7 +17,7 @@ mkin - 1.1.0 + 1.1.1

diff --git a/docs/articles/web_only/benchmarks.html b/docs/articles/web_only/benchmarks.html index 393d0218..2f7730bd 100644 --- a/docs/articles/web_only/benchmarks.html +++ b/docs/articles/web_only/benchmarks.html @@ -33,7 +33,7 @@ mkin - 1.1.0 + 1.1.1 @@ -105,7 +105,7 @@

Benchmark timings for mkin

Johannes Ranke

-

Last change 1 July 2022 (rebuilt 2022-07-01)

+

Last change 1 July 2022 (rebuilt 2022-07-08)

Source: vignettes/web_only/benchmarks.rmd @@ -309,6 +309,14 @@ 1.877 3.906 + +Linux +i7-4710MQ +4.2.1 +1.1.1 +1.644 +3.172 + @@ -453,6 +461,15 @@ 8.058 3.339 + +Linux +i7-4710MQ +4.2.1 +1.1.1 +1.230 +5.839 +2.444 + @@ -642,6 +659,18 @@ 2.302 3.463 + +Linux +i7-4710MQ +4.2.1 +1.1.1 +0.678 +1.095 +1.149 +3.247 +1.658 +2.472 + diff --git a/docs/articles/web_only/dimethenamid_2018.html b/docs/articles/web_only/dimethenamid_2018.html index 25fd9f9e..b020a7b0 100644 --- a/docs/articles/web_only/dimethenamid_2018.html +++ b/docs/articles/web_only/dimethenamid_2018.html @@ -33,7 +33,7 @@ mkin - 1.1.0 + 1.1.1 @@ -105,7 +105,7 @@

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

-

Last change 1 July 2022, built on 01 Jul 2022

+

Last change 1 July 2022, built on 08 Jul 2022

Source: vignettes/web_only/dimethenamid_2018.rmd @@ -178,7 +178,7 @@ Status of individual fits: dataset model Calke Borstel Flaach BBA 2.2 BBA 2.3 Elliot - DFOP OK OK C OK C OK + DFOP OK OK OK OK C OK OK: No warnings C: Optimisation did not converge: @@ -286,21 +286,23 @@ DMTA_0 97.99583 96.50079 99.4909 k1 0.06377 0.03432 0.0932 k2 0.00848 0.00444 0.0125 g 0.95701 0.91313 1.0009 -a.1 1.82141 1.65974 1.9831 -SD.DMTA_0 1.64787 0.45779 2.8379 +a.1 1.82141 1.60516 2.0377 +SD.DMTA_0 1.64787 0.45729 2.8384 SD.k1 0.57439 0.24731 0.9015 -SD.k2 0.03296 -2.50143 2.5673 -SD.g 1.10266 0.32371 1.8816 +SD.k2 0.03296 -2.50524 2.5712 +SD.g 1.10266 0.32354 1.8818

While the other parameters converge to credible values, the variance of k2 (omega2.k2) converges to a very small value. The printout of the saem.mmkin model shows that the estimated standard deviation of k2 across the population of soils (SD.k2) is ill-defined, indicating overparameterisation of this model.

When the DFOP model is fitted with the two-component error model, we also observe that the estimated variance of k2 becomes very small, while being ill-defined, as illustrated by the excessive confidence interval of SD.k2.

 f_parent_saemix_dfop_tc <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
 f_parent_saemix_dfop_tc_moreiter <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
-  control = saemix_control_moreiter, transformations = "saemix")
-plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")
+ control = saemix_control_moreiter, transformations = "saemix") +
Likelihood cannot be computed by Importance Sampling.
+
+plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")

-
+
 print(f_parent_saemix_dfop_tc)

 
Kinetic nonlinear mixed-effects model fit by SAEM
 Structural model:
@@ -316,21 +318,21 @@ Likelihood computed by importance sampling
   666 664   -323
 
 Fitted parameters:
-          estimate    lower    upper
-DMTA_0    98.27617  96.3088 100.2436
-k1         0.06437   0.0337   0.0950
-k2         0.00880   0.0063   0.0113
-g          0.95249   0.9100   0.9949
-a.1        1.06161   0.8625   1.2607
-b.1        0.02967   0.0226   0.0367
-SD.DMTA_0  2.06075   0.4187   3.7028
-SD.k1      0.59357   0.2561   0.9310
-SD.k2      0.00292 -10.2960  10.3019
-SD.g       1.05725   0.3808   1.7337

+          estimate     lower    upper
+DMTA_0    9.82e+01  96.27937 100.1783
+k1        6.41e-02   0.03333   0.0948
+k2        8.56e-03   0.00608   0.0110
+g         9.55e-01   0.91440   0.9947
+a.1       1.07e+00   0.86542   1.2647
+b.1       2.96e-02   0.02258   0.0367
+SD.DMTA_0 2.04e+00   0.40629   3.6678
+SD.k1     5.98e-01   0.25796   0.9373
+SD.k2     5.28e-04 -58.93251  58.9336
+SD.g      1.04e+00   0.36509   1.7083

Doubling the number of iterations in the first phase of the algorithm leads to a slightly lower likelihood, and therefore to slightly higher AIC and BIC values. With even more iterations, the algorithm stops with an error message. This is related to the variance of k2 approximating zero and has been submitted as a bug to the saemix package, as the algorithm does not converge in this case.

An alternative way to fit DFOP in combination with the two-component error model is to use the model formulation with transformed parameters as used per default in mkin. When using this option, convergence is slower, but eventually the algorithm stops as well with the same error message.

The four combinations (SFO/const, SFO/tc, DFOP/const and DFOP/tc) and the version with increased iterations can be compared using the model comparison function of the saemix package:

-
+
 AIC_parent_saemix <- saemix::compare.saemix(
   f_parent_saemix_sfo_const$so,
   f_parent_saemix_sfo_tc$so,
@@ -338,7 +340,7 @@ SD.g       1.05725   0.3808   1.7337

   f_parent_saemix_dfop_tc$so,
   f_parent_saemix_dfop_tc_moreiter$so)
Likelihoods calculated by importance sampling
-
+
 rownames(AIC_parent_saemix) <- c(
   "SFO const", "SFO tc", "DFOP const", "DFOP tc", "DFOP tc more iterations")
 print(AIC_parent_saemix)

@@ -346,10 +348,10 @@ SD.g       1.05725   0.3808   1.7337
SFO const 796.38 795.34 SFO tc 798.38 797.13 DFOP const 705.75 703.88 -DFOP tc 665.65 663.57 -DFOP tc more iterations 665.88 663.80 +DFOP tc 665.72 663.63 +DFOP tc more iterations NaN NaN

In order to check the influence of the likelihood calculation algorithms implemented in saemix, the likelihood from Gaussian quadrature is added to the best fit, and the AIC values obtained from the three methods are compared.

-
+
 f_parent_saemix_dfop_tc$so <-
   saemix::llgq.saemix(f_parent_saemix_dfop_tc$so)
 AIC_parent_saemix_methods <- c(
@@ -359,11 +361,11 @@ DFOP tc more iterations 665.88 663.80

 )
 print(AIC_parent_saemix_methods)
    is     gq    lin 
-665.65 665.68 665.11
+665.72 665.88 665.15

The AIC values based on importance sampling and Gaussian quadrature are very similar. Using linearisation is known to be less accurate, but still gives a similar value.

In order to illustrate that the comparison of the three method depends on the degree of convergence obtained in the fit, the same comparison is shown below for the fit using the defaults for the number of iterations and the number of MCMC chains.

When using OpenBlas for linear algebra, there is a large difference in the values obtained with Gaussian quadrature, so the larger number of iterations makes a lot of difference. When using the LAPACK version coming with Debian Bullseye, the AIC based on Gaussian quadrature is almost the same as the one obtained with the other methods, also when using defaults for the fit.

-
+
 f_parent_saemix_dfop_tc_defaults <- mkin::saem(f_parent_mkin_tc["DFOP", ])
 f_parent_saemix_dfop_tc_defaults$so <-
   saemix::llgq.saemix(f_parent_saemix_dfop_tc_defaults$so)
@@ -374,14 +376,14 @@ DFOP tc more iterations 665.88 663.80

 )
 print(AIC_parent_saemix_methods_defaults)
    is     gq    lin 
-668.27 718.36 666.49
+668.91 663.61 667.40

Comparison

The following table gives the AIC values obtained with both backend packages using the same control parameters (800 iterations burn-in, 300 iterations second phase, 15 chains).

-
+
 AIC_all <- data.frame(
   check.names = FALSE,
   "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
@@ -406,7 +408,7 @@ DFOP tc more iterations 665.88 663.80

 SFO
 const
 796.60
-796.60
+794.17
 796.38
 
 
@@ -420,15 +422,15 @@ DFOP tc more iterations 665.88 663.80
DFOP const NA -671.98 +704.95 705.75 DFOP tc 671.91 -665.11 -665.65 +665.15 +665.72 @@ -443,15 +445,15 @@ DFOP tc more iterations 665.88 663.80

Session Info

-
+
 
R version 4.2.1 (2022-06-23)
 Platform: x86_64-pc-linux-gnu (64-bit)
 Running under: Debian GNU/Linux 11 (bullseye)
 
 Matrix products: default
-BLAS:   /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3
-LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.13.so
+BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
+LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0
 
 locale:
  [1] LC_CTYPE=de_DE.UTF-8       LC_NUMERIC=C              
@@ -466,24 +468,24 @@ attached base packages:
 [8] base     
 
 other attached packages:
-[1] saemix_3.0   npde_3.2     nlme_3.1-158 mkin_1.1.0   knitr_1.39  
+[1] nlme_3.1-158 mkin_1.1.1   knitr_1.39  
 
 loaded via a namespace (and not attached):
  [1] deSolve_1.32      zoo_1.8-10        tidyselect_1.1.2  xfun_0.31        
  [5] bslib_0.3.1       purrr_0.3.4       lattice_0.20-45   colorspace_2.0-3 
- [9] vctrs_0.4.1       generics_0.1.2    htmltools_0.5.2   yaml_2.3.5       
-[13] utf8_1.2.2        rlang_1.0.3       pkgdown_2.0.5     jquerylib_0.1.4  
-[17] pillar_1.7.0      glue_1.6.2        DBI_1.1.3         lifecycle_1.0.1  
+ [9] vctrs_0.4.1       generics_0.1.3    htmltools_0.5.2   yaml_2.3.5       
+[13] utf8_1.2.2        rlang_1.0.3       pkgdown_2.0.5     saemix_3.0       
+[17] jquerylib_0.1.4   pillar_1.7.0      glue_1.6.2        lifecycle_1.0.1  
 [21] stringr_1.4.0     munsell_0.5.0     gtable_0.3.0      ragg_1.2.2       
-[25] codetools_0.2-18  memoise_2.0.1     evaluate_0.15     fastmap_1.1.0    
+[25] memoise_2.0.1     evaluate_0.15     npde_3.2          fastmap_1.1.0    
 [29] lmtest_0.9-40     fansi_1.0.3       highr_0.9         scales_1.2.0     
 [33] cachem_1.0.6      desc_1.4.1        jsonlite_1.8.0    systemfonts_1.0.4
-[37] fs_1.5.2          gridExtra_2.3     textshaping_0.3.6 ggplot2_3.3.6    
+[37] fs_1.5.2          textshaping_0.3.6 gridExtra_2.3     ggplot2_3.3.6    
 [41] digest_0.6.29     stringi_1.7.6     dplyr_1.0.9       grid_4.2.1       
 [45] rprojroot_2.0.3   cli_3.3.0         tools_4.2.1       magrittr_2.0.3   
 [49] sass_0.4.1        tibble_3.1.7      crayon_1.5.1      pkgconfig_2.0.3  
-[53] ellipsis_0.3.2    assertthat_0.2.1  rmarkdown_2.14    mclust_5.4.10    
-[57] R6_2.5.1          compiler_4.2.1   

+[53] ellipsis_0.3.2    rmarkdown_2.14    R6_2.5.1          mclust_5.4.10    
+[57] compiler_4.2.1

References diff --git a/docs/authors.html b/docs/authors.html index 998e6d54..afa0d11c 100644 --- a/docs/authors.html +++ b/docs/authors.html @@ -17,7 +17,7 @@ mkin - 1.1.0 + 1.1.1

@@ -109,13 +109,13 @@

Ranke J (2022). mkin: Kinetic Evaluation of Chemical Degradation Data. -R package version 1.1.0, https://pkgdown.jrwb.de/mkin/. +R package version 1.1.1, https://pkgdown.jrwb.de/mkin/. 

@Manual{,
   title = {mkin: Kinetic Evaluation of Chemical Degradation Data},
   author = {Johannes Ranke},
   year = {2022},
-  note = {R package version 1.1.0},
+  note = {R package version 1.1.1},
   url = {https://pkgdown.jrwb.de/mkin/},
 }
diff --git a/docs/index.html b/docs/index.html index 47775538..6e6a90fa 100644 --- a/docs/index.html +++ b/docs/index.html @@ -44,7 +44,7 @@ mkin - 1.1.0 + 1.1.1
diff --git a/docs/news/index.html b/docs/news/index.html index b8202e95..e7a7f571 100644 --- a/docs/news/index.html +++ b/docs/news/index.html @@ -17,7 +17,7 @@ mkin - 1.1.0 + 1.1.1
@@ -83,7 +83,8 @@

mkin 1.1.1

-

  • ‘vignettes/FOCUS_L.rmd’: Remove an outdated note referring to a failure to calculate the covariance matrix for DFOP with the L2 dataset. Since 0.9.45.5 the covariance matrix is available

    • +

    • ’R/{mkinmod,mkinpredict}.R: Store DLL information in mkinmod objects and use that information in mkinpredict to avoid a performance regression brought by a bugfix in R 4.2.x. Thanks to Tomas Kalibera for his analysis of the problem on the r-package-devel list and his suggestion on how to fix it.

      • +

    • ‘vignettes/FOCUS_L.rmd’: Remove an outdated note referring to a failure to calculate the covariance matrix for DFOP with the L2 dataset. Since 0.9.45.5 the covariance matrix is available

    • ‘vignettes/web_only/benchmarks.rmd’: Add the first benchmark data using my laptop system, therefore add the CPU when showing the benchmark results.

    • ‘dimethenamid_2018’: Update example code to use saemix

    • ‘CAKE_export’: Check for validity of the map argument, updates

      • diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml index bf228fe1..19332d6b 100644 --- a/docs/pkgdown.yml +++ b/docs/pkgdown.yml @@ -11,7 +11,7 @@ articles: benchmarks: web_only/benchmarks.html compiled_models: web_only/compiled_models.html dimethenamid_2018: web_only/dimethenamid_2018.html -last_built: 2022-07-01T11:17Z +last_built: 2022-07-08T15:33Z urls: reference: https://pkgdown.jrwb.de/mkin/reference article: https://pkgdown.jrwb.de/mkin/articles diff --git a/docs/reference/index.html b/docs/reference/index.html index 876207da..63e3de8f 100644 --- a/docs/reference/index.html +++ b/docs/reference/index.html @@ -17,7 +17,7 @@ mkin - 1.1.0 + 1.1.1
-- cgit v1.2.1